AN ALTERNATIVE PARAMETRIC APPROACH FOR DISCRETE MISSING DATA PROBLEMS

Abstract

We propose an iterative method of estimation for discrete missing data problems that is conceptually different from the Expectation–Maximization (EM) algorithm and that does not in general yield the observed data maximum likelihood estimate (MLE). The proposed approach is based conceptually upon weighting the set of possible complete-data MLEs. Its implementation avoids the expectation step of EM, which can sometimes be problematic. In the simple case of Bernoulli trials missing completely at random, the iterations of the proposed algorithm are equivalent to the EM iterations. For a familiar genetics-oriented multinomial problem with missing count data and for the motivating example with epidemiologic applications that involves a mixture of a left censored normal distribution with a point mass at zero, we investigate the finite sample performance of the proposed estimator and find it to be competitive with that of the MLE. We give some intuitive justification for the method, and we explore an interesting connection between our algorithm and multiple imputation in order to suggest an approach for estimating standard errors.

Keywords:

• Complete data
• Estimation
• Likelihood
• Multiple imputation
• Observed data

Acknowledgments